The town hall, moderated by Anderson Cooper, will be the first high-profile event for the leading third party to make a splash following the major party conventions in July.
The two former Republicans have a lot of work to do to make the official presidential debate stage in the fall, let alone the White House.
CNN's first Libertarian town hall was not necessarily the breakthrough event some libertarians had hoped for.
For one, Johnson's performance, running through talking points in the face of several emotional appeals from audience members, occasionally fell flat. For another, the event was overshadowed as Democrats took to the floor of the House of Representatives to protest the lack of legislative action on gun control.
Look to see whether Johnson connects with the audience and makes his proposals personal.
As for the event being overshadowed, anything is possible, but the governors can head into the town hall knowing at least this time, the House is in recess.
Show us the money? Koch aide says not likely
Two men who Johnson and Weld hope are watching: siblings by the names of Charles and David Koch.
The billionaire Kochs, unnerved by Trump's support for protectionism and mass deportations, were forced to push back this weekend in Colorado Springs against speculation from associates that they could support Hillary Clinton. Yet because they have not said how they personally will vote, some in their powerful network of donors are holding out hope that they will back the party that David Koch represented as vice president in 1980: the Libertarians.
But in an interview with CNN in Colorado this weekend, the Kochs' chief political aide, Mark Holden, poured some cold water on any official sign of support.
"I would be surprised if we did," Holden told CNN, conceding that he may have "good ideas" but that activating their network would not make the race winnable for the ticket. "My concern would be if people saw us go in on Johnson as a network, that would cause some concerns for people who maybe wanted us to go in on Trump."
Holden said that he and the ticket had not had any official contact.
Several Koch donors, however, have. A few told CNN that they did indeed plan to support him financially, with some considering giving to a new super PAC that formed last week by a Weld friend -- the Socially Liberal Fiscally Conservative Political Action Committee.
"That's the push right now: How do we get more name recognition?" said Chris Rufus, a California tomato processing executive who is supporting two separate Johnson super PACs. "So we're spending money on that."
Johnson and Weld have pitched themselves publicly to major Republican figures, including former Florida Gov. Jeb Bush and most pointedly, former Massachusetts Gov. Mitt Romney.
The Republican Party's 2012 presidential nominee has made clear he does not support Donald Trump and in an interview
with CNN's Wolf Blitzer, Romney said he was open to the idea of supporting Johnson. At the time, he praised Weld -- a Republican governor of Massachusetts before Romney's tenure -- but said he was turned off by Johnson's enthusiasm for marijuana legalization.
In an interview with CNN last week during the Democratic National Convention, Johnson said
he had spoken to Romney.
"I think he's considering the possibility of doing this," Johnson said, "of actually endorsing the two of us."
For his part, Weld said he didn't want to press Romney unless Johnson managed to move up a bit in the polls.
Johnson and Weld could seize this opportunity deliver a message geared towards the Republican establishment.
The Trump factor
Both Johnson and Weld grow animated at the Republican nominee's mention and call him nothing short of dangerous. Johnson frequently ticks off Trump's proposals as inhumane and irresponsible. Weld has even gone so far as to compare Trump's immigration plans to the Holocaust.
At the first Libertarian town hall, Weld said of Trump: "You cannot be a president of the United States and talk like that."
So given this ticket's record of slamming Trump, one can expect them not to pull any punches when his name comes up.
They will have a lot of recent news to work with as well, after Trump has spent several days feuding with the family of a Muslim soldier who was killed in action and suggested the US should warm up its relationship with Russia.
During the Democratic National Convention, Johnson stumbled into minor controversy over an interview he had with the Washington Examiner
. In the interview, he stated his support for legislation compelling businesses not to discriminate against LGBT people. But he came under fire for some comments he made trying to flesh out this stance.
"Under the guise of religious freedom, anybody can do anything. Back to Mormonism, why shouldn't somebody be able to shoot somebody else because their freedom of religion says that God has spoken to them?" Johnson said. "I just see religious freedom as a category, as just being a black hole."
The problem? Johnson's campaign is based out of the heavily Mormon and religiously conservative state of Utah. He has said he hopes to gain the support of Romney, a devout Mormon, and backing from other religious conservatives.
In a statement, Johnson called his comments "an admittedly very imprecise reference to the violence that accompanied the Mormon's early history in the 1800s."
This was a minor blip in two weeks' worth of steady press for the Johnson/Weld campaign, but the former governor of New Mexico still needs to make inroads with the religious community and cannot afford a major slip up like this in such a widely broadcast scenario.
If Johnson and Weld really want to make a splash, they need to capture Democratic votes, too.
Throughout the campaign, Johnson has made a play for Bernie Sanders supporters opposed to Hillary Clinton, a group which has emerged as one of the most sought after bloc of voters since Clinton's victory in California.
But Johnson and Weld, who has called Clinton a friend and sought an ambassadorship within President Bill Clinton's administration, have avoided attacking Clinton. Outside of casting her as part of the much-maligned Washington status quo, the former governors have reserved their sharpest critiques for Trump.
The latest CNN/ORC poll showed Sanders supporters going 69% for Clinton, 13% for Green Party candidate Jill Stein and 10% for Johnson.
On matters of policy, Johnson does not have a lot in common with Sanders relative to Clinton and Stein. Johnson could move to bridge the gap by hitting Clinton on her perceived dishonesty, the DNC leaks demonstrating institutional bias against Sanders and the email scandal from her time as secretary of state.